The earliest analysis of the magnetic moments of octet baryons in heavy baryon chiral perturbation theory to orders \(\mathcal {O}(m_q^{1/2})\)  and \(\mathcal {O}(m_q \ln m_q)\)  was presented in Ref. [1]}. There, it was concluded that, unlike the axial current case, the inclusion of intermediate decuplet baryons in the loops does not partially cancel the contribution from intermediate octet baryons. The use of the combined formalism in \(1/N_c\)  and quiral corrections has shed light on the subject [2]}, [3]} by allowing one to perform a rigorous analytical evaluation of the cancellations that follow from the large-\(N_c\)  spin-flavor symmetry of baryons. In Ref. [2]}, one-loop corrections to magnetic moments to relative order \(1/N_c^3\)  in the \(1/N_c\)  expansion were carried out under the limit \(\Delta \rightarrow 0\) , where \(\Delta \equiv M_T-M_B\)  is the average decuplet-octet mass difference. A more refined analysis was later presented in Ref. [3]}, where the assumption of degenerate intermediate baryons was lifted and explicit \(SU(3)\)  symmetry breaking effects were also included.
